Question: If $x \diamond y = 3x-y$ and $x \bigtriangleup y = x^{2}+2y^{2}$, find $-3 \bigtriangleup (-2 \diamond -4)$.
First, find $-2 \diamond -4$ $ -2 \diamond -4 = (3)(-2)-(-4)$ $ \hphantom{-2 \diamond -4} = -2$ Now, find $-3 \bigtriangleup -2$ $ -3 \bigtriangleup -2 = (-3)^{2}+2(-2)^{2}$ $ \hphantom{-3 \bigtriangleup -2} = 17$.